Pries: 619 Complex Variables II. Projects.

Pries: 619 Complex Variables II. Projects.
There are an enormous number of possible projects to choose from. Here are a couple topics
from Miranda that would be interesting. I’d be happy to help you choose a topic which
matches your interests.
Quality is more important than quantity but you could aim for a 20 minute talk and an
8 page paper. Make sure to have an introduction, theory, examples, pictures/graphs as
appropriate, and bibliography.
1. Miranda pg 67-70, 134-135, 143-145: Ramification divisors and Plucker’s formula.
2. Miranda pg 71-72, 98-102: Resolution of singularities and projections.
3. Miranda III.3: Group actions and bound on |Aut(X)| (Rodney?).
4. Miranda III.4: Monodromy (Galois theory).
5. Miranda V.4: Maps to projective space.
6. Proof of the Riemann-Roch theorem (other references might be easier).
7. Miranda VII.2: The canonical map and classification of curves.
8. Miranda pg 212-215 plus other references: Moduli spaces of curves of genus g.
9. Miranda VII.3: General position, Castelnuovo’s bound.
10. Miranda VII.4: Weierstrass points.
11. Modular curves (Number theory).